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Block #1,557,143

TWNLength 10β˜…β˜…β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 4/25/2016, 8:15:56 AM Β· Difficulty 10.6851 Β· 5,260,686 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
f6d46c7379a8df33bd11b405b9c38b723757a07cea2ee0f6489ff56b9ea426ba
View on Chainz β†—

Height

#1,557,143

Difficulty

10.685143

Transactions

2

Size

17.47 KB

Version

2

Bits

0aaf658a

Nonce

342,147,342

Timestamp

4/25/2016, 8:15:56 AM

Confirmations

5,260,686

Mined by

⛏️ P2SHANk8XWy5UHcC5cfymzmBJy5ioBGjHVAYRn

Merkle Root

f7dab971e33731e298765f26253e020589df36f7da057404083d25c003bd0012
Transactions (2)
Coinbaseb5313b00286634…975f8ad1aa0a8e
1 in β†’ 1 out9.0500 XPM110 B
ANk8XWy5…GjHVAYRn
a91d4912281ab0…ea983a63da18a3
119 in β†’ 2 out829.8312 XPM17.27 KB
AcUhv3NV…uD2e6UUsAQHE5e6H…xDwU3vYU
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.

1.179 Γ— 10⁹⁷(98-digit number)
11794050009257679894…70756085160667647999
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
1.179 Γ— 10⁹⁷(98-digit number)
11794050009257679894…70756085160667647999
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
1.179 Γ— 10⁹⁷(98-digit number)
11794050009257679894…70756085160667648001
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
2.358 Γ— 10⁹⁷(98-digit number)
23588100018515359788…41512170321335295999
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
2.358 Γ— 10⁹⁷(98-digit number)
23588100018515359788…41512170321335296001
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
4.717 Γ— 10⁹⁷(98-digit number)
47176200037030719577…83024340642670591999
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
4.717 Γ— 10⁹⁷(98-digit number)
47176200037030719577…83024340642670592001
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
9.435 Γ— 10⁹⁷(98-digit number)
94352400074061439154…66048681285341183999
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
9.435 Γ— 10⁹⁷(98-digit number)
94352400074061439154…66048681285341184001
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
1.887 Γ— 10⁹⁸(99-digit number)
18870480014812287830…32097362570682367999
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
1.887 Γ— 10⁹⁸(99-digit number)
18870480014812287830…32097362570682368001
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:57,786,696 XPMΒ·at block #6,817,828 Β· updates every 60s
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