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Block #680,066

TWNLength 11β˜…β˜…β˜…β˜†β˜†

Bi-Twin Chain Β· Discovered 8/16/2014, 10:57:15 AM Β· Difficulty 10.9626 Β· 6,127,417 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
a562d66d30f8cd6469f051045205e536bce473c66d4f7f2c8019d8a381a59523
View on Chainz β†—

Height

#680,066

Difficulty

10.962646

Transactions

1

Size

206 B

Version

2

Bits

0af66ffd

Nonce

1,292,075,594

Timestamp

8/16/2014, 10:57:15 AM

Confirmations

6,127,417

Mined by

⛏️ P2SHANSXnLY2HX2a5e6fdcDUZDtfwTSd25TjkD

Merkle Root

6cb42dc01190e956a36830568e80a50a9b8153f2333f744baa72f9154df5dbe8
Transactions (1)
Coinbase6cb42dc01190e9…72f9154df5dbe8
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.

2.371 Γ— 10⁹⁴(95-digit number)
23718943936473631534…89908250208456975519
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
2.371 Γ— 10⁹⁴(95-digit number)
23718943936473631534…89908250208456975519
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
2.371 Γ— 10⁹⁴(95-digit number)
23718943936473631534…89908250208456975521
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
4.743 Γ— 10⁹⁴(95-digit number)
47437887872947263069…79816500416913951039
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
4.743 Γ— 10⁹⁴(95-digit number)
47437887872947263069…79816500416913951041
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
9.487 Γ— 10⁹⁴(95-digit number)
94875775745894526139…59633000833827902079
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
9.487 Γ— 10⁹⁴(95-digit number)
94875775745894526139…59633000833827902081
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
1.897 Γ— 10⁹⁡(96-digit number)
18975155149178905227…19266001667655804159
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
1.897 Γ— 10⁹⁡(96-digit number)
18975155149178905227…19266001667655804161
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
3.795 Γ— 10⁹⁡(96-digit number)
37950310298357810455…38532003335311608319
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
3.795 Γ— 10⁹⁡(96-digit number)
37950310298357810455…38532003335311608321
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
7.590 Γ— 10⁹⁡(96-digit number)
75900620596715620911…77064006670623216639
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:57,703,891 XPMΒ·at block #6,807,482 Β· updates every 60s
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