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Block #52,138

TWNLength 9β˜…β˜†β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 7/16/2013, 8:59:17 AM Β· Difficulty 8.9082 Β· 6,758,329 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
35d9d7aaa4ac20cd6c1d7c5ad7656af23e3f79d05bd2cb53ea6e7f531689b7f4
View on Chainz β†—

Height

#52,138

Difficulty

8.908197

Transactions

1

Size

199 B

Version

2

Bits

08e87f9b

Nonce

360

Timestamp

7/16/2013, 8:59:17 AM

Confirmations

6,758,329

Mined by

⛏️ P2SHAZL9DFFiX7p5ZQXeqHANFph67vmwQY3vsF

Merkle Root

19b9e67c3fa340b4a9f0c6a83c07a2e10d7b27ebbf4525085626c2efd87aa4ab
Transactions (1)
Coinbase19b9e67c3fa340…26c2efd87aa4ab
1 in β†’ 1 out12.5800 XPM110 B
AZL9DFFi…mwQY3vsF
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.

1.257 Γ— 10⁹³(94-digit number)
12576725015529589311…25569037317986198289
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
1.257 Γ— 10⁹³(94-digit number)
12576725015529589311…25569037317986198289
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
1.257 Γ— 10⁹³(94-digit number)
12576725015529589311…25569037317986198291
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
2.515 Γ— 10⁹³(94-digit number)
25153450031059178622…51138074635972396579
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
2.515 Γ— 10⁹³(94-digit number)
25153450031059178622…51138074635972396581
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
5.030 Γ— 10⁹³(94-digit number)
50306900062118357244…02276149271944793159
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
5.030 Γ— 10⁹³(94-digit number)
50306900062118357244…02276149271944793161
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
1.006 Γ— 10⁹⁴(95-digit number)
10061380012423671448…04552298543889586319
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
1.006 Γ— 10⁹⁴(95-digit number)
10061380012423671448…04552298543889586321
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
2.012 Γ— 10⁹⁴(95-digit number)
20122760024847342897…09104597087779172639
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.

β˜…β˜†β˜†β˜†β˜†
Rarity
CommonChain length 9

Found in most blocks. The baseline for Primecoin's proof-of-work.

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
Cross-reference on Chainz Explorer
Circulating Supply:57,727,822 XPMΒ·at block #6,810,466 Β· updates every 60s
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