Block #257,032

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 11/12/2013, 5:17:15 AM · Difficulty 9.9755 · 6,557,806 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

f74c61e9674d8d9dad9607257fb544fc9bd536d052c046e5f60f1a61f766569a

View on Chainz ↗

Height

#257,032

Difficulty

9.975493

Transactions

Size

2.16 KB

Version

Bits

09f9b9e7

Nonce

23,316

Timestamp

11/12/2013, 5:17:15 AM

Confirmations

6,557,806

Mined by

⛏️ P2SHAZDUEbdSvp8cw8AAZ1fERZUqSYRYKMRZET

Merkle Root

1c81ec8c4e729f41c5639f929c80658466b07f5a14ff892b0d83f4f491ff3eb8

Transactions (5)

Coinbasee6a306803cfb21…d2a50ad54ba551

1 in → 2 out10.0800 XPM137 B

AZDUEbdS…RYKMRZET Abiw8n3q…ZnZfgvQW

41a837714d3776…b4984b0a092286

1 in → 4 out10.0800 XPM260 B

AYwTRdfJ…3whzbfUq AMUH1Z1t…Q1XW99zU AeKNrjNj…1NEq95Ta ARvs7MTe…jqQUrZ7v

25e608e8b6a557…8f58a1d0f1adf7

6 in → 2 out92.9057 XPM968 B

AQUKapCU…NN8rogcU AX65w2u1…U9FMmnRi

bed5894b6af752…59c6a257fb31ad

1 in → 6 out12.2375 XPM361 B

AVHcc9zb…JkngbvXL AJ6Fiu6B…tbWLzJrw ATMFDrtE…5yZxmv57 AHbGXzeD…A3SKohbN AVg5YGji…Aq7MMxRC

60dbb8207e11bd…eb4048646fe8d2

1 in → 7 out7.7500 XPM396 B

AVGgSJVH…QFfLHvEe ASZ68fuZ…vBt8Luhr AZKgQwBY…rTXiwBnJ AVvBfWAv…s7d3svTc AazQqwHc…a1Spx1VN

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.

6.560 × 10⁹⁴(95-digit number)

65605602561714810841…03467649025114927599

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

6.560 × 10⁹⁴(95-digit number)

65605602561714810841…03467649025114927599

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

6.560 × 10⁹⁴(95-digit number)

65605602561714810841…03467649025114927601

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

1.312 × 10⁹⁵(96-digit number)

13121120512342962168…06935298050229855199

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.312 × 10⁹⁵(96-digit number)

13121120512342962168…06935298050229855201

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

2.624 × 10⁹⁵(96-digit number)

26242241024685924336…13870596100459710399

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

2.624 × 10⁹⁵(96-digit number)

26242241024685924336…13870596100459710401

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

5.248 × 10⁹⁵(96-digit number)

52484482049371848673…27741192200919420799

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

5.248 × 10⁹⁵(96-digit number)

52484482049371848673…27741192200919420801

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

1.049 × 10⁹⁶(97-digit number)

10496896409874369734…55482384401838841599

Verify on FactorDB ↗Wolfram Alpha ↗

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 — 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

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 × 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 #257,032

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