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Block #278,682

TWNLength 10β˜…β˜…β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 11/28/2013, 2:04:17 AM Β· Difficulty 9.9696 Β· 6,521,855 confirmations

TWN
Bi-Twin Chain

Interleaved pairs of primes that differ by 2, forming twin prime pairs at each level.

Block Header
Block Hash
3835315f9f5ad1bb7d12347977fbb1cb1ae9efa035eea1b2f41cfdbb988b3309
View on Chainz β†—

Height

#278,682

Difficulty

9.969596

Transactions

1

Size

236 B

Version

2

Bits

09f83773

Nonce

4,008

Timestamp

11/28/2013, 2:04:17 AM

Confirmations

6,521,855

Merkle Root

b1fe1c856d963623e3c5bbb8f4fde2ff373bb484878e071c5156258831940a68
Transactions (1)
Coinbaseb1fe1c856d9636…56258831940a68
1 in β†’ 2 out10.0500 XPM142 B
AKcbk49N…GJbKa7j1AHsw4d6U…EnM8UXNZ
Prime Chain Origin

This is the prime chain origin stored in the block header. It is a composite number (not prime itself) β€” it equals the first prime in the chain multiplied by a primorial. The origin anchors the entire chain to this specific block.

6.214 Γ— 10¹⁰³(104-digit number)
62144335070059042810…30003254777471987360
Discovered Prime Numbers
Lower: 2^k Γ— origin βˆ’ 1 | Upper: 2^k Γ— origin + 1

These are the actual prime numbers discovered by this block, computed using the verified Primecoin formula. Each number has been independently confirmed to pass the Fermat primality test. Use the FactorDB links to verify any number independently.

Level 0 β€” Twin Prime Pair (origin Β± 1)
origin βˆ’ 1
6.214 Γ— 10¹⁰³(104-digit number)
62144335070059042810…30003254777471987359
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
6.214 Γ— 10¹⁰³(104-digit number)
62144335070059042810…30003254777471987361
Verify on FactorDB β†—Wolfram Alpha β†—
Difference: origin + 1 βˆ’ origin βˆ’ 1 = 2 (twin primes βœ“)
Level 1 β€” Twin Prime Pair (2^1 Γ— origin Β± 1)
2^1 Γ— origin βˆ’ 1
1.242 Γ— 10¹⁰⁴(105-digit number)
12428867014011808562…60006509554943974719
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
1.242 Γ— 10¹⁰⁴(105-digit number)
12428867014011808562…60006509554943974721
Verify on FactorDB β†—Wolfram Alpha β†—
Difference: 2^1 Γ— origin + 1 βˆ’ 2^1 Γ— origin βˆ’ 1 = 2 (twin primes βœ“)
Level 2 β€” Twin Prime Pair (2^2 Γ— origin Β± 1)
2^2 Γ— origin βˆ’ 1
2.485 Γ— 10¹⁰⁴(105-digit number)
24857734028023617124…20013019109887949439
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
2.485 Γ— 10¹⁰⁴(105-digit number)
24857734028023617124…20013019109887949441
Verify on FactorDB β†—Wolfram Alpha β†—
Difference: 2^2 Γ— origin + 1 βˆ’ 2^2 Γ— origin βˆ’ 1 = 2 (twin primes βœ“)
Level 3 β€” Twin Prime Pair (2^3 Γ— origin Β± 1)
2^3 Γ— origin βˆ’ 1
4.971 Γ— 10¹⁰⁴(105-digit number)
49715468056047234248…40026038219775898879
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
4.971 Γ— 10¹⁰⁴(105-digit number)
49715468056047234248…40026038219775898881
Verify on FactorDB β†—Wolfram Alpha β†—
Difference: 2^3 Γ— origin + 1 βˆ’ 2^3 Γ— origin βˆ’ 1 = 2 (twin primes βœ“)
Level 4 β€” Twin Prime Pair (2^4 Γ— origin Β± 1)
2^4 Γ— origin βˆ’ 1
9.943 Γ— 10¹⁰⁴(105-digit number)
99430936112094468497…80052076439551797759
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
9.943 Γ— 10¹⁰⁴(105-digit number)
99430936112094468497…80052076439551797761
Verify on FactorDB β†—Wolfram Alpha β†—
Difference: 2^4 Γ— origin + 1 βˆ’ 2^4 Γ— origin βˆ’ 1 = 2 (twin primes βœ“)

What this block proved

The miner who found this block proved the existence of 10 consecutive prime numbers forming a Bi-Twin Chain. The prime chain origin β€” the large number shown above β€” anchors the chain and is divisible by a primorial (the product of small primes), cryptographically tying these prime numbers to this specific block.

View full Prime Chain Discovery page β†’
β˜…β˜…β˜†β˜†β˜†
Rarity
UncommonChain length 10
How Primecoin's Proof-of-Work Constructs These Primes

Primecoin stores a value called the prime chain origin in each block. The miner found a large integer such that when divided by a primorial (the product of small primes: 2 Γ— 3 Γ— 5 Γ— 7 Γ— …), the result is the first prime in the chain. The origin is deliberately divisible by this primorial β€” that divisibility is part of the proof.

Prime Chain Origin = First Prime Γ— Primorial (2Β·3Β·5Β·7Β·11·…)
Source: Primecoin prime.cpp β€” CheckPrimeProofOfWork()

This is why the origin has many small prime factors β€” those factors are the primorial divisor. The chain then extends from the first prime using the TWN formula:

TWN: twin pairs (p, p+2) where p = origin/primorial βˆ’ 1 and p+2 = origin/primorial + 1
Verify on a Primecoin Node

Anyone running a Primecoin node can independently verify this block using the following RPC commands. Run these from the primecoin-cli command line or via the debug console in the Primecoin wallet.

1. Get block hash by height
getblockhash 278682

Returns the block hash for a given block height. Use this to confirm the hash shown above matches the chain.

2. Get full block data
getblock 3835315f9f5ad1bb7d12347977fbb1cb1ae9efa035eea1b2f41cfdbb988b3309

Returns the full block header including difficulty, prime chain origin, prime chain type, transaction IDs, and all other fields shown on this page.

How to run these commands: To verify this data independently, open a terminal on your own Primecoin node and run primecoin-cli <command>. Alternatively, open the Primecoin-Qt wallet, go to Help β†’ Debug Window β†’ Console, and type the command directly. The node must be fully synced to this block height for the commands to return results.

Cross-reference on Chainz Explorer

Chainz is an independent Primecoin block explorer. Compare this block's data to verify accuracy.

View Block #278,682 on Chainz β†—
Circulating Supply:57,648,358 XPMΒ·at block #6,800,536 Β· updates every 60s
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