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Block #1,406,639

TWNLength 10β˜…β˜…β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 1/10/2016, 1:05:22 AM Β· Difficulty 10.8066 Β· 5,435,324 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
00973e4d5d3ad411ae712e3bdef06f452fe8045fe5ce418f76ee64434eb63c2e
View on Chainz β†—

Height

#1,406,639

Difficulty

10.806637

Transactions

2

Size

425 B

Version

2

Bits

0ace7fbf

Nonce

688,633,144

Timestamp

1/10/2016, 1:05:22 AM

Confirmations

5,435,324

Mined by

⛏️ P2SHAW5bnQbqFe476KJ3BvMZyikGxb6Rh12sS1

Merkle Root

3f3815947dd031d28639ea419fcd9943fee8a103c3f5fe11ef16e8124f53a281
Transactions (2)
Coinbase4281864b1f8ab8…8094d41e974217
1 in β†’ 1 out8.5600 XPM109 B
AW5bnQbq…6Rh12sS1
58ccc0067bc4d6…efe7f2cbc9f12c
1 in β†’ 2 out159655.8177 XPM225 B
AQz5cxT1…6bpmEdXYAMquSwf2…Esarybq5
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.

2.702 Γ— 10⁹⁷(98-digit number)
27024574755093391678…19636993907584491519
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
2.702 Γ— 10⁹⁷(98-digit number)
27024574755093391678…19636993907584491519
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
2.702 Γ— 10⁹⁷(98-digit number)
27024574755093391678…19636993907584491521
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
5.404 Γ— 10⁹⁷(98-digit number)
54049149510186783357…39273987815168983039
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
5.404 Γ— 10⁹⁷(98-digit number)
54049149510186783357…39273987815168983041
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
1.080 Γ— 10⁹⁸(99-digit number)
10809829902037356671…78547975630337966079
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
1.080 Γ— 10⁹⁸(99-digit number)
10809829902037356671…78547975630337966081
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
2.161 Γ— 10⁹⁸(99-digit number)
21619659804074713343…57095951260675932159
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
2.161 Γ— 10⁹⁸(99-digit number)
21619659804074713343…57095951260675932161
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
4.323 Γ— 10⁹⁸(99-digit number)
43239319608149426686…14191902521351864319
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
4.323 Γ— 10⁹⁸(99-digit number)
43239319608149426686…14191902521351864321
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:57,980,086 XPMΒ·at block #6,841,962 Β· updates every 60s
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