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Block #1,338,784

TWNLength 11β˜…β˜…β˜…β˜†β˜†

Bi-Twin Chain Β· Discovered 11/24/2015, 1:53:33 AM Β· Difficulty 10.7950 Β· 5,485,984 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
5c0335a06e5187389d787b9a5138c768223dff654403b1916fde78b07923baae
View on Chainz β†—

Height

#1,338,784

Difficulty

10.794984

Transactions

2

Size

8.66 KB

Version

2

Bits

0acb8415

Nonce

419,619,366

Timestamp

11/24/2015, 1:53:33 AM

Confirmations

5,485,984

Mined by

⛏️ P2SHAQBj3d6khS52StB5nNb7YWWPTNMfF3Jo1e

Merkle Root

67d0ca56b0edf0ff1591f141e8abaff6879a01b070fcf0f2cccb18fec326a75e
Transactions (2)
Coinbase2be636328c5c95…5fdb31e12135dc
1 in β†’ 1 out8.6800 XPM109 B
AQBj3d6k…MfF3Jo1e
b5a2a7685bfba5…f081d9bfa9594c
58 in β†’ 2 out1404.9400 XPM8.46 KB
AS8hfvj6…u5uXwtZsAYFmLAJb…b6YRpBoo
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.

6.856 Γ— 10⁹³(94-digit number)
68569576758259295675…33769146458125951999
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
6.856 Γ— 10⁹³(94-digit number)
68569576758259295675…33769146458125951999
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
6.856 Γ— 10⁹³(94-digit number)
68569576758259295675…33769146458125952001
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
1.371 Γ— 10⁹⁴(95-digit number)
13713915351651859135…67538292916251903999
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
1.371 Γ— 10⁹⁴(95-digit number)
13713915351651859135…67538292916251904001
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
2.742 Γ— 10⁹⁴(95-digit number)
27427830703303718270…35076585832503807999
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
2.742 Γ— 10⁹⁴(95-digit number)
27427830703303718270…35076585832503808001
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
5.485 Γ— 10⁹⁴(95-digit number)
54855661406607436540…70153171665007615999
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
5.485 Γ— 10⁹⁴(95-digit number)
54855661406607436540…70153171665007616001
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
1.097 Γ— 10⁹⁡(96-digit number)
10971132281321487308…40306343330015231999
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
1.097 Γ— 10⁹⁡(96-digit number)
10971132281321487308…40306343330015232001
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
2.194 Γ— 10⁹⁡(96-digit number)
21942264562642974616…80612686660030463999
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:57,842,215 XPMΒ·at block #6,824,767 Β· updates every 60s
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