Block #975,341

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 3/15/2015, 8:03:11 AM · Difficulty 10.8485 · 5,833,749 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

94da90c51e479de31fe1a029dfba28ff70194c03d739b15364ccd9d8a77bfa31

View on Chainz ↗

Height

#975,341

Difficulty

10.848477

Transactions

Size

1.42 KB

Version

Bits

0ad935d1

Nonce

409,344,390

Timestamp

3/15/2015, 8:03:11 AM

Confirmations

5,833,749

Mined by

⛏️ P2SHATqxqqbSxQ8Tg8n22gQPmANbhiDNfHHMZw

Merkle Root

8c5bdb3264cb54833d6508c7e6befc73975d3dc3232e9da1b68a3356400c7de5

Transactions (2)

Coinbaseb564474d24af9a…7900418e2d5430

1 in → 1 out8.5000 XPM109 B

ATqxqqbS…DNfHHMZw

b4fbd158c9b196…22d6e95400e504

8 in → 2 out121.2071 XPM1.23 KB

AarS4gCN…StCmdcQQ ANwDoxeL…KT7kjVdN

Prime Chain Origin

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

2.938 × 10⁹³(94-digit number)

29385406623770512926…24577492879334458879

Discovered Prime Numbers

Lower: 2^k × origin − 1 | Upper: 2^k × 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 — Twin Prime Pair (origin ± 1)

origin − 1

2.938 × 10⁹³(94-digit number)

29385406623770512926…24577492879334458879

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

2.938 × 10⁹³(94-digit number)

29385406623770512926…24577492879334458881

Verify on FactorDB ↗Wolfram Alpha ↗

Difference: origin + 1 − origin − 1 = 2 (twin primes ✓)

Level 1 — Twin Prime Pair (2^1 × origin ± 1)

2^1 × origin − 1

5.877 × 10⁹³(94-digit number)

58770813247541025853…49154985758668917759

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

5.877 × 10⁹³(94-digit number)

58770813247541025853…49154985758668917761

Verify on FactorDB ↗Wolfram Alpha ↗

Difference: 2^1 × origin + 1 − 2^1 × origin − 1 = 2 (twin primes ✓)

Level 2 — Twin Prime Pair (2^2 × origin ± 1)

2^2 × origin − 1

1.175 × 10⁹⁴(95-digit number)

11754162649508205170…98309971517337835519

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.175 × 10⁹⁴(95-digit number)

11754162649508205170…98309971517337835521

Verify on FactorDB ↗Wolfram Alpha ↗

Difference: 2^2 × origin + 1 − 2^2 × origin − 1 = 2 (twin primes ✓)

Level 3 — Twin Prime Pair (2^3 × origin ± 1)

2^3 × origin − 1

2.350 × 10⁹⁴(95-digit number)

23508325299016410341…96619943034675671039

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

2.350 × 10⁹⁴(95-digit number)

23508325299016410341…96619943034675671041

Verify on FactorDB ↗Wolfram Alpha ↗

Difference: 2^3 × origin + 1 − 2^3 × origin − 1 = 2 (twin primes ✓)

Level 4 — Twin Prime Pair (2^4 × origin ± 1)

2^4 × origin − 1

4.701 × 10⁹⁴(95-digit number)

47016650598032820683…93239886069351342079

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

4.701 × 10⁹⁴(95-digit number)

47016650598032820683…93239886069351342081

Verify on FactorDB ↗Wolfram Alpha ↗

Difference: 2^4 × origin + 1 − 2^4 × origin − 1 = 2 (twin primes ✓)

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 — the large number shown above — anchors the chain and is divisible by a primorial (the product of small primes), cryptographically tying these prime numbers to this specific block.

★★☆☆☆

Rarity

UncommonChain length 10

Roughly 1 in 100 blocks. Solid but expected in a healthy network.

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 × 3 × 5 × 7 × …), the result is the first prime in the chain. The origin is deliberately divisible by this primorial — that divisibility is part of the proof.

Prime Chain Origin = First Prime × Primorial (2·3·5·7·11·…)

Source: Primecoin prime.cpp — CheckPrimeProofOfWork()

This is why the origin has many small prime factors — 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 − 1 and p+2 = origin/primorial + 1

Cross-reference on Chainz Explorer

Block #975,341

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