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Block #1,678,343

TWNLength 10β˜…β˜…β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 7/18/2016, 11:10:11 AM Β· Difficulty 10.6938 Β· 5,159,108 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
712a0dcf5395d50beb672e78d75ce37e0fa8696a6074b35f5bf714af4f66f425
View on Chainz β†—

Height

#1,678,343

Difficulty

10.693818

Transactions

1

Size

201 B

Version

2

Bits

0ab19e08

Nonce

66,411,151

Timestamp

7/18/2016, 11:10:11 AM

Confirmations

5,159,108

Mined by

⛏️ P2SHARJ6SF5fF1f4BWNVX8yiGN3EQjm9SzDDQ4

Merkle Root

5822ff121ff7bd7b473d0d1bcf2ed1ef908074022c76d9064ac1c2faa40d8e74
Transactions (1)
Coinbase5822ff121ff7bd…c1c2faa40d8e74
1 in β†’ 1 out8.7300 XPM109 B
ARJ6SF5f…m9SzDDQ4
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.

2.343 Γ— 10⁹⁸(99-digit number)
23433095424477095476…46799336727794483199
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
2.343 Γ— 10⁹⁸(99-digit number)
23433095424477095476…46799336727794483199
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
2.343 Γ— 10⁹⁸(99-digit number)
23433095424477095476…46799336727794483201
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
4.686 Γ— 10⁹⁸(99-digit number)
46866190848954190953…93598673455588966399
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
4.686 Γ— 10⁹⁸(99-digit number)
46866190848954190953…93598673455588966401
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
9.373 Γ— 10⁹⁸(99-digit number)
93732381697908381906…87197346911177932799
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
9.373 Γ— 10⁹⁸(99-digit number)
93732381697908381906…87197346911177932801
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
1.874 Γ— 10⁹⁹(100-digit number)
18746476339581676381…74394693822355865599
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
1.874 Γ— 10⁹⁹(100-digit number)
18746476339581676381…74394693822355865601
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
3.749 Γ— 10⁹⁹(100-digit number)
37492952679163352762…48789387644711731199
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
3.749 Γ— 10⁹⁹(100-digit number)
37492952679163352762…48789387644711731201
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:57,943,932 XPMΒ·at block #6,837,450 Β· updates every 60s
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