Block #268,507

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 11/22/2013, 5:05:56 AM · Difficulty 9.9569 · 6,539,597 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

ea4b07e9743f5ff559b849c6fb9f24fad7a1fe08f874db3b82d815527bdee49f

View on Chainz ↗

Height

#268,507

Difficulty

9.956887

Transactions

Size

7.00 KB

Version

Bits

09f4f68e

Nonce

3,543

Timestamp

11/22/2013, 5:05:56 AM

Confirmations

6,539,597

Mined by

⛏️ P2SHAKcbk49N7DP3nse7MJr3Ed6rZiGJbKa7j1

Merkle Root

d0d4221e09f02f94854a0ffec8b96172819a0cf73387696353ab616e0768a1d4

Transactions (5)

Coinbase8cf46f299e2f44…e923a7564511d9

1 in → 2 out10.1618 XPM141 B

AKcbk49N…GJbKa7j1 ALfEGCwh…VawujfMm

5c2eae8f161b4d…cf47504c9fc330

5 in → 2 out20.0881 XPM817 B

AJbftSkX…YoNi6ifL AJqU19SL…XiUu62Xe

476ddf9950979f…8a6d8e7474e273

1 in → 2 out99.4900 XPM227 B

AKizwuXD…aWVJKbgR AX65w2u1…U9FMmnRi

769ba534da59ca…a5fe9a473803d3

1 in → 2 out13.7101 XPM226 B

AVLKkHky…jJmWzHdV ATYKvUGi…Qx8fH8R8

e284144aa2e474…b73cfe5e494aa4

38 in → 1 out4.7000 XPM5.54 KB

AP4G5Aiy…MZgQSmXp

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.

3.540 × 10¹⁰²(103-digit number)

35402516581671705305…92420821952608494099

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

3.540 × 10¹⁰²(103-digit number)

35402516581671705305…92420821952608494099

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

3.540 × 10¹⁰²(103-digit number)

35402516581671705305…92420821952608494101

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

7.080 × 10¹⁰²(103-digit number)

70805033163343410610…84841643905216988199

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

7.080 × 10¹⁰²(103-digit number)

70805033163343410610…84841643905216988201

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

1.416 × 10¹⁰³(104-digit number)

14161006632668682122…69683287810433976399

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.416 × 10¹⁰³(104-digit number)

14161006632668682122…69683287810433976401

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

2.832 × 10¹⁰³(104-digit number)

28322013265337364244…39366575620867952799

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

2.832 × 10¹⁰³(104-digit number)

28322013265337364244…39366575620867952801

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

5.664 × 10¹⁰³(104-digit number)

56644026530674728488…78733151241735905599

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 #268,507

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