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Block #64,240

TWNLength 8β˜…β˜†β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 7/19/2013, 6:28:08 AM Β· Difficulty 8.9812 Β· 6,736,831 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
6fb7ebe1303054cd41c16df3b544568db2cf6c15ec4d123b82a23f75bcb9817d
View on Chainz β†—

Height

#64,240

Difficulty

8.981169

Transactions

1

Size

198 B

Version

2

Bits

08fb2dec

Nonce

125

Timestamp

7/19/2013, 6:28:08 AM

Confirmations

6,736,831

Merkle Root

000e6d6dafdb2974f76f202b39509908b2bc2c2fa349a4333982c4dd07fcef4f
Transactions (1)
Coinbase000e6d6dafdb29…82c4dd07fcef4f
1 in β†’ 1 out12.3800 XPM109 B
AbD6bSgy…JVXAE8Yf
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.

1.552 Γ— 10⁹³(94-digit number)
15529279680617562686…53256750847272577920
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
1.552 Γ— 10⁹³(94-digit number)
15529279680617562686…53256750847272577919
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
1.552 Γ— 10⁹³(94-digit number)
15529279680617562686…53256750847272577921
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
3.105 Γ— 10⁹³(94-digit number)
31058559361235125372…06513501694545155839
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
3.105 Γ— 10⁹³(94-digit number)
31058559361235125372…06513501694545155841
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
6.211 Γ— 10⁹³(94-digit number)
62117118722470250744…13027003389090311679
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
6.211 Γ— 10⁹³(94-digit number)
62117118722470250744…13027003389090311681
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
1.242 Γ— 10⁹⁴(95-digit number)
12423423744494050148…26054006778180623359
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
1.242 Γ— 10⁹⁴(95-digit number)
12423423744494050148…26054006778180623361
Verify on FactorDB β†—Wolfram Alpha β†—
Difference: 2^3 Γ— origin + 1 βˆ’ 2^3 Γ— origin βˆ’ 1 = 2 (twin primes βœ“)

What this block proved

The miner who found this block proved the existence of 8 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 8
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 64240

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 6fb7ebe1303054cd41c16df3b544568db2cf6c15ec4d123b82a23f75bcb9817d

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 #64,240 on Chainz β†—
Circulating Supply:57,652,630 XPMΒ·at block #6,801,070 Β· updates every 60s
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