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Block #1,538,993

TWNLength 10β˜…β˜…β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 4/13/2016, 6:20:37 AM Β· Difficulty 10.6335 Β· 5,270,962 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
ccfb8961fd7a6a71839cabfda64a75d52618f003146a56647cda33f08fb42f72
View on Chainz β†—

Height

#1,538,993

Difficulty

10.633457

Transactions

2

Size

2.00 KB

Version

2

Bits

0aa22a35

Nonce

375,600,830

Timestamp

4/13/2016, 6:20:37 AM

Confirmations

5,270,962

Mined by

⛏️ P2SHAaRRhe1S7S9JUbZGjC2tYFCJL4aRwoC7WQ

Merkle Root

8c1d41819b77f4a271d3940fa5512b0ec503545b538a2e7815725e546269c0a2
Transactions (2)
Coinbase5ba7095b9921a0…99d3d0a330dd41
1 in β†’ 1 out8.8500 XPM109 B
AaRRhe1S…aRwoC7WQ
a7fe538cf4a48f…f0afa70971b30e
12 in β†’ 2 out100.9270 XPM1.81 KB
APvps6gj…BD7NJi1RAWF4rtPp…LnbQHVaN
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.

5.543 Γ— 10⁹⁴(95-digit number)
55430912168859372306…77302771871242948399
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
5.543 Γ— 10⁹⁴(95-digit number)
55430912168859372306…77302771871242948399
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
5.543 Γ— 10⁹⁴(95-digit number)
55430912168859372306…77302771871242948401
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
1.108 Γ— 10⁹⁡(96-digit number)
11086182433771874461…54605543742485896799
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
1.108 Γ— 10⁹⁡(96-digit number)
11086182433771874461…54605543742485896801
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
2.217 Γ— 10⁹⁡(96-digit number)
22172364867543748922…09211087484971793599
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
2.217 Γ— 10⁹⁡(96-digit number)
22172364867543748922…09211087484971793601
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
4.434 Γ— 10⁹⁡(96-digit number)
44344729735087497845…18422174969943587199
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
4.434 Γ— 10⁹⁡(96-digit number)
44344729735087497845…18422174969943587201
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
8.868 Γ— 10⁹⁡(96-digit number)
88689459470174995690…36844349939887174399
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
8.868 Γ— 10⁹⁡(96-digit number)
88689459470174995690…36844349939887174401
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:57,723,721 XPMΒ·at block #6,809,954 Β· updates every 60s
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AQZeJoQ81VgeHQBpEYTgvNqV1gnz3L5SvK

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