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Block #1,496,291

TWNLength 10β˜…β˜…β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 3/14/2016, 11:14:22 AM Β· Difficulty 10.6459 Β· 5,337,443 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
0ac858c49b5a74edfa5f069d0214f469a1190f00417acd586ea599e5778c583a
View on Chainz β†—

Height

#1,496,291

Difficulty

10.645854

Transactions

2

Size

573 B

Version

2

Bits

0aa556a8

Nonce

48,110,528

Timestamp

3/14/2016, 11:14:22 AM

Confirmations

5,337,443

Mined by

⛏️ P2SHAZd3kEczF7XPCeeSHYvkzK2ZtXeGQ8NQ5z

Merkle Root

c0bfaeaf44675e19001cce759469d91bb19f51fe064059ecc734dfda61738923
Transactions (2)
Coinbase1ed528065514a8…2cb34daa7799c3
1 in β†’ 1 out8.8200 XPM109 B
AZd3kEcz…eGQ8NQ5z
d960408de32af1…50c477bfd310f7
2 in β†’ 2 out0.5188 XPM373 B
AUSESZ8f…nMdFDc5iAd4jhMck…D7VhWYLf
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.

5.403 Γ— 10⁹⁷(98-digit number)
54036251986389786925…62292287722098278399
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
5.403 Γ— 10⁹⁷(98-digit number)
54036251986389786925…62292287722098278399
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
5.403 Γ— 10⁹⁷(98-digit number)
54036251986389786925…62292287722098278401
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
1.080 Γ— 10⁹⁸(99-digit number)
10807250397277957385…24584575444196556799
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
1.080 Γ— 10⁹⁸(99-digit number)
10807250397277957385…24584575444196556801
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
2.161 Γ— 10⁹⁸(99-digit number)
21614500794555914770…49169150888393113599
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
2.161 Γ— 10⁹⁸(99-digit number)
21614500794555914770…49169150888393113601
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
4.322 Γ— 10⁹⁸(99-digit number)
43229001589111829540…98338301776786227199
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
4.322 Γ— 10⁹⁸(99-digit number)
43229001589111829540…98338301776786227201
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
8.645 Γ— 10⁹⁸(99-digit number)
86458003178223659081…96676603553572454399
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
8.645 Γ— 10⁹⁸(99-digit number)
86458003178223659081…96676603553572454401
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:57,914,096 XPMΒ·at block #6,833,733 Β· updates every 60s
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