Block #277,973

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 11/27/2013, 7:20:21 PM · Difficulty 9.9677 · 6,528,769 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

4dc9d22b4420879a419f5df56bd091a851dfdc828f7e485164686fb06816b764

View on Chainz ↗

Height

#277,973

Difficulty

9.967673

Transactions

Size

1.73 KB

Version

Bits

09f7b96e

Nonce

7,771

Timestamp

11/27/2013, 7:20:21 PM

Confirmations

6,528,769

Mined by

⛏️ P2SHAKcbk49N7DP3nse7MJr3Ed6rZiGJbKa7j1

Merkle Root

2c4a4d70adc7d98e409cffaa4539366f9529b0d24fd538a2f6073884d8bfa544

Transactions (5)

Coinbase4db67aac25cb7c…1339611191a617

1 in → 2 out10.0900 XPM142 B

AKcbk49N…GJbKa7j1 AHsw4d6U…EnM8UXNZ

67e71cdb701f2a…ff4b80ce6b15c2

3 in → 4 out1150.5060 XPM590 B

AcFsz2ip…rWoZ6pjL AWEdAFip…yK8FjeBr AajErXr7…7qV9qiZa ARo32Xqg…2DSaRuZA

b3314ca8b0ca96…6b23b13e510b75

1 in → 2 out10.0600 XPM192 B

AZwXD8Y4…82pDxeJp ANoTnkHU…YDa5XqJD

0bd42c1ec68e5e…1068bbdb0292b9

3 in → 2 out9.4178 XPM523 B

AYPJKBAP…Pw1QhDNy AUPNjwz5…2sReE1ne

0b57f46f21ba4c…b1832d529607fd

1 in → 2 out0.5311 XPM226 B

AHF4R1cd…9uUbcAxw ARSZXFiK…36hSCqKC

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.

1.510 × 10¹⁰⁵(106-digit number)

15102752940574089276…64129850665733667839

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

1.510 × 10¹⁰⁵(106-digit number)

15102752940574089276…64129850665733667839

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.510 × 10¹⁰⁵(106-digit number)

15102752940574089276…64129850665733667841

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

3.020 × 10¹⁰⁵(106-digit number)

30205505881148178552…28259701331467335679

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

3.020 × 10¹⁰⁵(106-digit number)

30205505881148178552…28259701331467335681

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

6.041 × 10¹⁰⁵(106-digit number)

60411011762296357105…56519402662934671359

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

6.041 × 10¹⁰⁵(106-digit number)

60411011762296357105…56519402662934671361

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

1.208 × 10¹⁰⁶(107-digit number)

12082202352459271421…13038805325869342719

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.208 × 10¹⁰⁶(107-digit number)

12082202352459271421…13038805325869342721

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

2.416 × 10¹⁰⁶(107-digit number)

24164404704918542842…26077610651738685439

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 #277,973

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