Block #600,867

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 6/25/2014, 2:22:50 AM · Difficulty 10.9160 · 6,209,710 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

89162ed150e66a3d13168d1d61d1afc19544d690dadabba70e861c1f40427883

View on Chainz ↗

Height

#600,867

Difficulty

10.915951

Transactions

Size

1.27 KB

Version

Bits

0aea7bbd

Nonce

264,914

Timestamp

6/25/2014, 2:22:50 AM

Confirmations

6,209,710

Mined by

AQvZBsUoAqCaKecR1VEueWTuBchppgRZTJ

Merkle Root

e7d448ef0da4ae535d1493add76a4093cac83a627f8c218da568d3d3797f67a4

Transactions (4)

Coinbase4fa23a06242e0d…966ca2dd66bbec

1 in → 14 out8.3800 XPM538 B

AQvZBsUo…hppgRZTJ AJzWx2VD…j4ZSMit5 AJtNW28X…Syb4Ph5j AQyr8Lw3…hs4nt3Pn AGhWLwcW…XVrQp7o8

627f297cb215b7…8f09227d4ee760

1 in → 2 out6.7544 XPM225 B

ALREN6bU…BEnBVbPM Ae7YXEyn…hnSYZsCr

0f6cbd00eb01ac…4517784d72d4dd

1 in → 2 out6.2727 XPM226 B

AQj3K98w…Sszmm2Zt Acb4eCGa…av3Gcjrq

bb17334ff3e97d…86a85876fb1193

1 in → 2 out4.1454 XPM226 B

AS9ZCvju…bu3NEFwZ AKdaM5tD…Nh2h8YSK

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.

2.409 × 10⁹³(94-digit number)

24094996375315411199…15625348257909849599

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

2.409 × 10⁹³(94-digit number)

24094996375315411199…15625348257909849599

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

2.409 × 10⁹³(94-digit number)

24094996375315411199…15625348257909849601

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

4.818 × 10⁹³(94-digit number)

48189992750630822398…31250696515819699199

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

4.818 × 10⁹³(94-digit number)

48189992750630822398…31250696515819699201

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

9.637 × 10⁹³(94-digit number)

96379985501261644796…62501393031639398399

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

9.637 × 10⁹³(94-digit number)

96379985501261644796…62501393031639398401

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

1.927 × 10⁹⁴(95-digit number)

19275997100252328959…25002786063278796799

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.927 × 10⁹⁴(95-digit number)

19275997100252328959…25002786063278796801

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

3.855 × 10⁹⁴(95-digit number)

38551994200504657918…50005572126557593599

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

3.855 × 10⁹⁴(95-digit number)

38551994200504657918…50005572126557593601

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

Block #600,867

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