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Block #781,958

TWNLength 10β˜…β˜…β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 10/25/2014, 4:26:28 AM Β· Difficulty 10.9750 Β· 6,022,239 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
a393a420c2c388151d0d7ab7a706afa3143a98144aa3efb6e678e7ccf86d4ba4
View on Chainz β†—

Height

#781,958

Difficulty

10.974952

Transactions

2

Size

880 B

Version

2

Bits

0af99672

Nonce

1,036,640,769

Timestamp

10/25/2014, 4:26:28 AM

Confirmations

6,022,239

Mined by

⛏️ P2SHANSXnLY2HX2a5e6fdcDUZDtfwTSd25TjkD

Merkle Root

7f9d51e477ae8e0ad94661ecc20f076406e5ee988a683e3d79dfa3ea3a6ee72a
Transactions (2)
Coinbase2e2032497ea60f…5e706c8ead2880
1 in β†’ 1 out8.3000 XPM116 B
ANSXnLY2…Sd25TjkD
d43d17a09111a3…d38fb566610460
4 in β†’ 2 out798.3102 XPM672 B
AKUSPDHg…crr5eW9EAQUC7Hue…LL2XMoNY
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.

3.461 Γ— 10⁹⁸(99-digit number)
34615046312629182901…22454627970232934399
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
3.461 Γ— 10⁹⁸(99-digit number)
34615046312629182901…22454627970232934399
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
3.461 Γ— 10⁹⁸(99-digit number)
34615046312629182901…22454627970232934401
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
6.923 Γ— 10⁹⁸(99-digit number)
69230092625258365803…44909255940465868799
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
6.923 Γ— 10⁹⁸(99-digit number)
69230092625258365803…44909255940465868801
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
1.384 Γ— 10⁹⁹(100-digit number)
13846018525051673160…89818511880931737599
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
1.384 Γ— 10⁹⁹(100-digit number)
13846018525051673160…89818511880931737601
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
2.769 Γ— 10⁹⁹(100-digit number)
27692037050103346321…79637023761863475199
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
2.769 Γ— 10⁹⁹(100-digit number)
27692037050103346321…79637023761863475201
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
5.538 Γ— 10⁹⁹(100-digit number)
55384074100206692642…59274047523726950399
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
5.538 Γ— 10⁹⁹(100-digit number)
55384074100206692642…59274047523726950401
Verify on FactorDB β†—Wolfram Alpha β†—
Difference: 2^4 Γ— origin + 1 βˆ’ 2^4 Γ— origin βˆ’ 1 = 2 (twin primes βœ“)

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 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
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 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:57,677,623 XPMΒ·at block #6,804,196 Β· updates every 60s
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