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Block #1,317,756

TWNLength 10β˜…β˜…β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 11/8/2015, 1:51:58 AM Β· Difficulty 10.8619 Β· 5,523,708 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
7f5e508dfed72069373c2469b0c68d6d4042972263c661632c144e3980fc9c09
View on Chainz β†—

Height

#1,317,756

Difficulty

10.861852

Transactions

2

Size

16.03 KB

Version

2

Bits

0adca259

Nonce

759,920,863

Timestamp

11/8/2015, 1:51:58 AM

Confirmations

5,523,708

Mined by

⛏️ P2SHAbWs2zAJdcqMDYNjzf1xAdpFtPbkfh7ZmD

Merkle Root

58996550e42bc44d39539dd8e275627f27afa60e5064f89f7790acaa3c730326
Transactions (2)
Coinbase13eb6a3c6801a8…99fbefea5c9fac
1 in β†’ 1 out8.6400 XPM110 B
AbWs2zAJ…bkfh7ZmD
67c608a5bc7872…e9669e3f169dd0
109 in β†’ 2 out300000.0100 XPM15.83 KB
AatWo3Rs…8c41o3ZHAYKArr5V…V9VqiqCZ
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.

1.436 Γ— 10⁹⁷(98-digit number)
14368640573691924196…43406343725154096639
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
1.436 Γ— 10⁹⁷(98-digit number)
14368640573691924196…43406343725154096639
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
1.436 Γ— 10⁹⁷(98-digit number)
14368640573691924196…43406343725154096641
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
2.873 Γ— 10⁹⁷(98-digit number)
28737281147383848392…86812687450308193279
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
2.873 Γ— 10⁹⁷(98-digit number)
28737281147383848392…86812687450308193281
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
5.747 Γ— 10⁹⁷(98-digit number)
57474562294767696784…73625374900616386559
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
5.747 Γ— 10⁹⁷(98-digit number)
57474562294767696784…73625374900616386561
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
1.149 Γ— 10⁹⁸(99-digit number)
11494912458953539356…47250749801232773119
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
1.149 Γ— 10⁹⁸(99-digit number)
11494912458953539356…47250749801232773121
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
2.298 Γ— 10⁹⁸(99-digit number)
22989824917907078713…94501499602465546239
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
2.298 Γ— 10⁹⁸(99-digit number)
22989824917907078713…94501499602465546241
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:57,976,085 XPMΒ·at block #6,841,463 Β· updates every 60s
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