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Block #139,105

TWNLength 9β˜…β˜†β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 8/28/2013, 7:25:57 PM Β· Difficulty 9.8298 Β· 6,677,932 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
50b5d63c82f14663720143cfacf609ebfbdeef0d0fc075e5dd053a72c1c7db73
View on Chainz β†—

Height

#139,105

Difficulty

9.829789

Transactions

1

Size

197 B

Version

2

Bits

09d46d0c

Nonce

164,827

Timestamp

8/28/2013, 7:25:57 PM

Confirmations

6,677,932

Merkle Root

26f854a8ef7a7c0b9f1d2e497ba4034e17f0976e984d6cf5dcf841f1b51be3f2
Transactions (1)
Coinbase26f854a8ef7a7c…f841f1b51be3f2
1 in β†’ 1 out10.3300 XPM109 B
ASki8pmA…Dwetzr7b
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.

1.936 Γ— 10⁹⁰(91-digit number)
19369760825819745961…67139136372893608620
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
1.936 Γ— 10⁹⁰(91-digit number)
19369760825819745961…67139136372893608619
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
1.936 Γ— 10⁹⁰(91-digit number)
19369760825819745961…67139136372893608621
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
3.873 Γ— 10⁹⁰(91-digit number)
38739521651639491922…34278272745787217239
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
3.873 Γ— 10⁹⁰(91-digit number)
38739521651639491922…34278272745787217241
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
7.747 Γ— 10⁹⁰(91-digit number)
77479043303278983845…68556545491574434479
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
7.747 Γ— 10⁹⁰(91-digit number)
77479043303278983845…68556545491574434481
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
1.549 Γ— 10⁹¹(92-digit number)
15495808660655796769…37113090983148868959
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
1.549 Γ— 10⁹¹(92-digit number)
15495808660655796769…37113090983148868961
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
3.099 Γ— 10⁹¹(92-digit number)
30991617321311593538…74226181966297737919
Verify on FactorDB β†—Wolfram Alpha β†—

What this block proved

The miner who found this block proved the existence of 9 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
CommonChain length 9
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 139105

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 50b5d63c82f14663720143cfacf609ebfbdeef0d0fc075e5dd053a72c1c7db73

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 #139,105 on Chainz β†—
Circulating Supply:57,780,327 XPMΒ·at block #6,817,036 Β· updates every 60s
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