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Block #680,109

TWNLength 11β˜…β˜…β˜…β˜†β˜†

Bi-Twin Chain Β· Discovered 8/16/2014, 11:40:37 AM Β· Difficulty 10.9627 Β· 6,133,744 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
90e73bfd80b7bd88f9d3d2fb4b9b901d32844932338cc95f7b0d7fa5e8bbd962
View on Chainz β†—

Height

#680,109

Difficulty

10.962651

Transactions

1

Size

207 B

Version

2

Bits

0af67051

Nonce

56,457,518

Timestamp

8/16/2014, 11:40:37 AM

Confirmations

6,133,744

Mined by

⛏️ P2SHANSXnLY2HX2a5e6fdcDUZDtfwTSd25TjkD

Merkle Root

670d22936c5f64eb72209ea55a457105b33c578a821a4543f1403962b8cba82b
Transactions (1)
Coinbase670d22936c5f64…403962b8cba82b
1 in β†’ 1 out8.3100 XPM116 B
ANSXnLY2…Sd25TjkD
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.

1.657 Γ— 10⁹⁢(97-digit number)
16578494828955640715…71306091111316662799
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
1.657 Γ— 10⁹⁢(97-digit number)
16578494828955640715…71306091111316662799
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
1.657 Γ— 10⁹⁢(97-digit number)
16578494828955640715…71306091111316662801
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
3.315 Γ— 10⁹⁢(97-digit number)
33156989657911281430…42612182222633325599
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
3.315 Γ— 10⁹⁢(97-digit number)
33156989657911281430…42612182222633325601
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
6.631 Γ— 10⁹⁢(97-digit number)
66313979315822562860…85224364445266651199
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
6.631 Γ— 10⁹⁢(97-digit number)
66313979315822562860…85224364445266651201
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
1.326 Γ— 10⁹⁷(98-digit number)
13262795863164512572…70448728890533302399
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
1.326 Γ— 10⁹⁷(98-digit number)
13262795863164512572…70448728890533302401
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
2.652 Γ— 10⁹⁷(98-digit number)
26525591726329025144…40897457781066604799
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
2.652 Γ— 10⁹⁷(98-digit number)
26525591726329025144…40897457781066604801
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
5.305 Γ— 10⁹⁷(98-digit number)
53051183452658050288…81794915562133209599
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:57,754,895 XPMΒ·at block #6,813,852 Β· updates every 60s
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