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Block #2,292,094

TWNLength 11β˜…β˜…β˜…β˜†β˜†

Bi-Twin Chain Β· Discovered 9/11/2017, 1:12:28 PM Β· Difficulty 10.9550 Β· 4,551,027 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
a742042670c579ed92f33324c70d73d766520bc6b3cfae039c1eee40426615b8
View on Chainz β†—

Height

#2,292,094

Difficulty

10.955005

Transactions

2

Size

426 B

Version

2

Bits

0af47b36

Nonce

17,813,058

Timestamp

9/11/2017, 1:12:28 PM

Confirmations

4,551,027

Mined by

⛏️ P2SHAeEEpXGvjPw8E7aTFevQwcCrvJKepSMs7Z

Merkle Root

032ba79f6f08d45f9b6a7b77920aad526e60ceb1db1d45345a3b7ef04e12f634
Transactions (2)
Coinbase3e46b30229f9d6…9f150d9a70cee9
1 in β†’ 1 out8.3300 XPM110 B
AeEEpXGv…KepSMs7Z
d10966dfaf6780…f3370a32f29617
1 in β†’ 2 out6929.9800 XPM226 B
AVAg57bi…Zcew2QsvAViBaKwf…3Xk3qwK8
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.

1.767 Γ— 10⁹⁴(95-digit number)
17675517266411164993…28940745076435665299
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
1.767 Γ— 10⁹⁴(95-digit number)
17675517266411164993…28940745076435665299
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
1.767 Γ— 10⁹⁴(95-digit number)
17675517266411164993…28940745076435665301
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
3.535 Γ— 10⁹⁴(95-digit number)
35351034532822329986…57881490152871330599
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
3.535 Γ— 10⁹⁴(95-digit number)
35351034532822329986…57881490152871330601
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
7.070 Γ— 10⁹⁴(95-digit number)
70702069065644659973…15762980305742661199
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
7.070 Γ— 10⁹⁴(95-digit number)
70702069065644659973…15762980305742661201
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
1.414 Γ— 10⁹⁡(96-digit number)
14140413813128931994…31525960611485322399
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
1.414 Γ— 10⁹⁡(96-digit number)
14140413813128931994…31525960611485322401
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
2.828 Γ— 10⁹⁡(96-digit number)
28280827626257863989…63051921222970644799
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
2.828 Γ— 10⁹⁡(96-digit number)
28280827626257863989…63051921222970644801
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
5.656 Γ— 10⁹⁡(96-digit number)
56561655252515727979…26103842445941289599
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:57,989,333 XPMΒ·at block #6,843,120 Β· updates every 60s
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