Block #463,254

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 3/27/2014, 11:47:06 PM · Difficulty 10.4173 · 6,332,870 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

ab0e4a559a44c4d0a7093600ff1f9c4f01c7c7a42d6f37a9ea1aedd38299739c

View on Chainz ↗

Height

#463,254

Difficulty

10.417290

Transactions

Size

6.70 KB

Version

Bits

0a6ad38c

Nonce

102,892

Timestamp

3/27/2014, 11:47:06 PM

Confirmations

6,332,870

Mined by

⛏️ P2SHAeKNrjNjtSncLJjUrDnQbrfzMS1NEq95Ta

Merkle Root

bae18e2261bc3640b5c95fc3e92a90a583f70c680452bed6cbc4ab20a608bc2b

Transactions (4)

Coinbase31d71e7a095b99…7f0af5a8d094f0

1 in → 1 out9.2800 XPM110 B

AeKNrjNj…1NEq95Ta

d7bb6d065ed752…1b1c627f7368a5

37 in → 2 out115.0856 XPM5.42 KB

ASCHyxo7…GJF8cxvQ AL7ukwsr…8JzBsnTQ

ce52b88dd4a6b1…4d32b9204fa4cd

2 in → 6 out18.3700 XPM442 B

AM6gM9HS…1AH2U2yH AWjvkJwz…JbcQNttY AQDGVS66…1PTWdWkm AeKNrjNj…1NEq95Ta AafXBxi8…MTbj7rvU

b1bed722775972…459fd82079a553

4 in → 2 out0.9199 XPM667 B

APKFuAjQ…QNRQcsus ANA654SS…XXR89mDn

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.

2.900 × 10¹⁰²(103-digit number)

29004215960191982752…89136465258043146239

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

2.900 × 10¹⁰²(103-digit number)

29004215960191982752…89136465258043146239

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

2.900 × 10¹⁰²(103-digit number)

29004215960191982752…89136465258043146241

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

5.800 × 10¹⁰²(103-digit number)

58008431920383965504…78272930516086292479

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

5.800 × 10¹⁰²(103-digit number)

58008431920383965504…78272930516086292481

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

1.160 × 10¹⁰³(104-digit number)

11601686384076793100…56545861032172584959

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.160 × 10¹⁰³(104-digit number)

11601686384076793100…56545861032172584961

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

2.320 × 10¹⁰³(104-digit number)

23203372768153586201…13091722064345169919

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

2.320 × 10¹⁰³(104-digit number)

23203372768153586201…13091722064345169921

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

4.640 × 10¹⁰³(104-digit number)

46406745536307172403…26183444128690339839

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

4.640 × 10¹⁰³(104-digit number)

46406745536307172403…26183444128690339841

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