Block #456,292

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 3/23/2014, 3:16:14 AM · Difficulty 10.4159 · 6,343,041 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

18ae0acaf2bfbb093d1fcbcbb2646c0aaa917562badf7f632b4fcb0b8082a468

View on Chainz ↗

Height

#456,292

Difficulty

10.415895

Transactions

Size

1.44 KB

Version

Bits

0a6a7817

Nonce

9,686

Timestamp

3/23/2014, 3:16:14 AM

Confirmations

6,343,041

Mined by

⛏️ P2SHAeKNrjNjtSncLJjUrDnQbrfzMS1NEq95Ta

Merkle Root

662a33fb8d6484910694abb7709150e8818761bd43324382c051015052b19155

Transactions (5)

Coinbase0ebc7f7ae432da…89db8c3f5f6030

1 in → 1 out9.2400 XPM110 B

AeKNrjNj…1NEq95Ta

66496ed0f15450…bd6428ce7c8dce

3 in → 5 out12.7216 XPM589 B

AKTw6wQF…qmT7dSwn AeKNrjNj…1NEq95Ta AeR5xAAu…QS19drpA AcBvLaSu…X3gaHvJ1 ANQKf2g4…29NaVj23

3107e1854b61f9…88bfd0c2f2f1df

1 in → 2 out7.1890 XPM227 B

AawEacRj…cTARxHM5 AMsrZhpd…pYrYdaoi

d5c74dc2461643…1e189fce00cef9

1 in → 2 out5.6301 XPM225 B

ASHkXkoh…4DpyBRLu Ab45HuDa…PBaTv6sz

39bbac700d0672…da3aab66308d5b

1 in → 2 out4.3660 XPM227 B

Ac3aiRgM…z1NXTBEd AZNo283Y…vXhRs8F8

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.

1.530 × 10¹⁰²(103-digit number)

15300784517216384386…67741483143314956799

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

1.530 × 10¹⁰²(103-digit number)

15300784517216384386…67741483143314956799

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.530 × 10¹⁰²(103-digit number)

15300784517216384386…67741483143314956801

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

3.060 × 10¹⁰²(103-digit number)

30601569034432768772…35482966286629913599

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

3.060 × 10¹⁰²(103-digit number)

30601569034432768772…35482966286629913601

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

6.120 × 10¹⁰²(103-digit number)

61203138068865537545…70965932573259827199

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

6.120 × 10¹⁰²(103-digit number)

61203138068865537545…70965932573259827201

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

1.224 × 10¹⁰³(104-digit number)

12240627613773107509…41931865146519654399

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.224 × 10¹⁰³(104-digit number)

12240627613773107509…41931865146519654401

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

2.448 × 10¹⁰³(104-digit number)

24481255227546215018…83863730293039308799

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

2.448 × 10¹⁰³(104-digit number)

24481255227546215018…83863730293039308801

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