Block #745,387

TWNLength 11★★★☆☆

Bi-Twin Chain · Discovered 9/28/2014, 10:42:39 PM · Difficulty 10.9793 · 6,063,535 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

8298b7c5264dd4b2ff548961b809d9c9c02a039be0b5485b7434b759e5b70ef6

View on Chainz ↗

Height

#745,387

Difficulty

10.979340

Transactions

Size

3.22 KB

Version

Bits

0afab60e

Nonce

1,135,826,663

Timestamp

9/28/2014, 10:42:39 PM

Confirmations

6,063,535

Mined by

⛏️ P2SHANSXnLY2HX2a5e6fdcDUZDtfwTSd25TjkD

Merkle Root

3f090b261551e8790f6bf03fa13a89ab63ea78443b916126007a44cb30d21778

Transactions (5)

Coinbasec677b9fce538a3…119282fd341f7f

1 in → 1 out8.3400 XPM116 B

ANSXnLY2…Sd25TjkD

d3735afb77a0c8…75fe1a4ae2c46f

1 in → 2 out8.4700 XPM191 B

AKTE6dSA…PJEXFrPD ARezZb4y…FxP7ivbi

221166a1e80789…be4a6fcd3cee9e

1 in → 2 out8.2700 XPM226 B

AXiN448S…vbShp5d5 AH7vxfTq…fBb6g4qH

09fc8634cdf323…e72af58dd933cb

16 in → 2 out4.1500 XPM2.39 KB

AXhHfWpj…isTLSNhS ARezZb4y…FxP7ivbi

6a49c6f366f205…2967f1a75999d3

1 in → 2 out6.6970 XPM225 B

AJncx5fY…2dwUF95j AFv8jiXE…b4pgdkLW

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.

1.074 × 10⁹⁵(96-digit number)

10743422742723090257…28211850363047691799

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

1.074 × 10⁹⁵(96-digit number)

10743422742723090257…28211850363047691799

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.074 × 10⁹⁵(96-digit number)

10743422742723090257…28211850363047691801

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

2.148 × 10⁹⁵(96-digit number)

21486845485446180514…56423700726095383599

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

2.148 × 10⁹⁵(96-digit number)

21486845485446180514…56423700726095383601

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

4.297 × 10⁹⁵(96-digit number)

42973690970892361029…12847401452190767199

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

4.297 × 10⁹⁵(96-digit number)

42973690970892361029…12847401452190767201

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

8.594 × 10⁹⁵(96-digit number)

85947381941784722058…25694802904381534399

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

8.594 × 10⁹⁵(96-digit number)

85947381941784722058…25694802904381534401

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

1.718 × 10⁹⁶(97-digit number)

17189476388356944411…51389605808763068799

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.718 × 10⁹⁶(97-digit number)

17189476388356944411…51389605808763068801

Verify on FactorDB ↗Wolfram Alpha ↗

Difference: 2^4 × origin + 1 − 2^4 × origin − 1 = 2 (twin primes ✓)

Level 5 — Twin Prime Pair (2^5 × origin ± 1)

2^5 × origin − 1

3.437 × 10⁹⁶(97-digit number)

34378952776713888823…02779211617526137599

Verify on FactorDB ↗Wolfram Alpha ↗

What this block proved

The miner who found this block proved the existence of 11 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

RareChain length 11

Approximately 1 in 1,000 blocks. Noteworthy discoveries.

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 #745,387

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