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Block #1,534,544

TWNLength 10β˜…β˜…β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 4/10/2016, 7:50:29 AM Β· Difficulty 10.6168 Β· 5,279,848 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
53b69c0cb22333bd31aa64029eab0ebe8473fa0fc079d2d0948db70602814e9f
View on Chainz β†—

Height

#1,534,544

Difficulty

10.616760

Transactions

2

Size

7.62 KB

Version

2

Bits

0a9de402

Nonce

543,335,762

Timestamp

4/10/2016, 7:50:29 AM

Confirmations

5,279,848

Mined by

⛏️ P2SHAMt5gp5GH4P2S5TLiJQGjSCgGNaGh8dZGe

Merkle Root

02f986ab79e162f61b60ad68ff731d0277049c1e1afcb4c5a91f7c945faf6baf
Transactions (2)
Coinbased2382139f72ae5…e4b493f1ebe98c
1 in β†’ 1 out8.9400 XPM110 B
AMt5gp5G…aGh8dZGe
655ca4a78a95b7…b51a5bd59bcaf8
51 in β†’ 1 out2840.8166 XPM7.42 KB
AKm24Syp…D9ZtPdbX
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.

2.995 Γ— 10⁹⁢(97-digit number)
29959300951692705259…38452105825266073599
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
2.995 Γ— 10⁹⁢(97-digit number)
29959300951692705259…38452105825266073599
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
2.995 Γ— 10⁹⁢(97-digit number)
29959300951692705259…38452105825266073601
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
5.991 Γ— 10⁹⁢(97-digit number)
59918601903385410518…76904211650532147199
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
5.991 Γ— 10⁹⁢(97-digit number)
59918601903385410518…76904211650532147201
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
1.198 Γ— 10⁹⁷(98-digit number)
11983720380677082103…53808423301064294399
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
1.198 Γ— 10⁹⁷(98-digit number)
11983720380677082103…53808423301064294401
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
2.396 Γ— 10⁹⁷(98-digit number)
23967440761354164207…07616846602128588799
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
2.396 Γ— 10⁹⁷(98-digit number)
23967440761354164207…07616846602128588801
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
4.793 Γ— 10⁹⁷(98-digit number)
47934881522708328414…15233693204257177599
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
4.793 Γ— 10⁹⁷(98-digit number)
47934881522708328414…15233693204257177601
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:57,759,198 XPMΒ·at block #6,814,391 Β· updates every 60s
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