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Block #857,257

TWNLength 11β˜…β˜…β˜…β˜†β˜†

Bi-Twin Chain Β· Discovered 12/17/2014, 5:09:21 PM Β· Difficulty 10.9676 Β· 5,979,498 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
09b9b542ba65365e199c0653711bc7748e9bf2913e5856c04e4f47169d92e5f4
View on Chainz β†—

Height

#857,257

Difficulty

10.967571

Transactions

2

Size

433 B

Version

2

Bits

0af7b2b9

Nonce

623,998,238

Timestamp

12/17/2014, 5:09:21 PM

Confirmations

5,979,498

Mined by

⛏️ P2SHANSXnLY2HX2a5e6fdcDUZDtfwTSd25TjkD

Merkle Root

0031a56cb5b68c59776a384fc23c3c2468a16907a8fe4dc416f31f2a9c5e1b14
Transactions (2)
Coinbasebac33aeb73119e…55ebe2e4ea1417
1 in β†’ 1 out8.3150 XPM116 B
ANSXnLY2…Sd25TjkD
867aa496deb831…efec2bee30b297
1 in β†’ 2 out0.0912 XPM226 B
AbD5ADL3…AzqK57vAAJsmXgXN…5iZQtoR1
Prime Chain Origin

This is the prime chain origin stored in the block header. It is a composite number (not prime itself) β€” it equals the first prime in the chain multiplied by a primorial. The origin anchors the entire chain to this specific block.

6.705 Γ— 10⁹⁡(96-digit number)
67057481437396457463…83113804093645601039
Discovered Prime Numbers
Lower: 2^k Γ— origin βˆ’ 1 | Upper: 2^k Γ— 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 β€” Twin Prime Pair (origin Β± 1)
origin βˆ’ 1
6.705 Γ— 10⁹⁡(96-digit number)
67057481437396457463…83113804093645601039
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
6.705 Γ— 10⁹⁡(96-digit number)
67057481437396457463…83113804093645601041
Verify on FactorDB β†—Wolfram Alpha β†—
Difference: origin + 1 βˆ’ origin βˆ’ 1 = 2 (twin primes βœ“)
Level 1 β€” Twin Prime Pair (2^1 Γ— origin Β± 1)
2^1 Γ— origin βˆ’ 1
1.341 Γ— 10⁹⁢(97-digit number)
13411496287479291492…66227608187291202079
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
1.341 Γ— 10⁹⁢(97-digit number)
13411496287479291492…66227608187291202081
Verify on FactorDB β†—Wolfram Alpha β†—
Difference: 2^1 Γ— origin + 1 βˆ’ 2^1 Γ— origin βˆ’ 1 = 2 (twin primes βœ“)
Level 2 β€” Twin Prime Pair (2^2 Γ— origin Β± 1)
2^2 Γ— origin βˆ’ 1
2.682 Γ— 10⁹⁢(97-digit number)
26822992574958582985…32455216374582404159
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
2.682 Γ— 10⁹⁢(97-digit number)
26822992574958582985…32455216374582404161
Verify on FactorDB β†—Wolfram Alpha β†—
Difference: 2^2 Γ— origin + 1 βˆ’ 2^2 Γ— origin βˆ’ 1 = 2 (twin primes βœ“)
Level 3 β€” Twin Prime Pair (2^3 Γ— origin Β± 1)
2^3 Γ— origin βˆ’ 1
5.364 Γ— 10⁹⁢(97-digit number)
53645985149917165970…64910432749164808319
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
5.364 Γ— 10⁹⁢(97-digit number)
53645985149917165970…64910432749164808321
Verify on FactorDB β†—Wolfram Alpha β†—
Difference: 2^3 Γ— origin + 1 βˆ’ 2^3 Γ— origin βˆ’ 1 = 2 (twin primes βœ“)
Level 4 β€” Twin Prime Pair (2^4 Γ— origin Β± 1)
2^4 Γ— origin βˆ’ 1
1.072 Γ— 10⁹⁷(98-digit number)
10729197029983433194…29820865498329616639
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
1.072 Γ— 10⁹⁷(98-digit number)
10729197029983433194…29820865498329616641
Verify on FactorDB β†—Wolfram Alpha β†—
Difference: 2^4 Γ— origin + 1 βˆ’ 2^4 Γ— origin βˆ’ 1 = 2 (twin primes βœ“)
Level 5 β€” Twin Prime Pair (2^5 Γ— origin Β± 1)
2^5 Γ— origin βˆ’ 1
2.145 Γ— 10⁹⁷(98-digit number)
21458394059966866388…59641730996659233279
Verify on FactorDB β†—Wolfram Alpha β†—

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 β€” the large number shown above β€” anchors the chain and is divisible by a primorial (the product of small primes), cryptographically tying these prime numbers to this specific block.

β˜…β˜…β˜…β˜†β˜†
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 Γ— 3 Γ— 5 Γ— 7 Γ— …), the result is the first prime in the chain. The origin is deliberately divisible by this primorial β€” that divisibility is part of the proof.

Prime Chain Origin = First Prime Γ— Primorial (2Β·3Β·5Β·7Β·11·…)
Source: Primecoin prime.cpp β€” CheckPrimeProofOfWork()

This is why the origin has many small prime factors β€” 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 βˆ’ 1 and p+2 = origin/primorial + 1
Cross-reference on Chainz Explorer
Circulating Supply:57,938,327 XPMΒ·at block #6,836,754 Β· updates every 60s
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