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Block #537,280

TWNLength 11β˜…β˜…β˜…β˜†β˜†

Bi-Twin Chain Β· Discovered 5/11/2014, 7:21:14 PM Β· Difficulty 10.9151 Β· 6,279,583 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
776ff18d886f2672965b30cd887700fe35bd417298766828fffdb4560e8122fe
View on Chainz β†—

Height

#537,280

Difficulty

10.915074

Transactions

1

Size

208 B

Version

2

Bits

0aea4251

Nonce

11,793,066

Timestamp

5/11/2014, 7:21:14 PM

Confirmations

6,279,583

Mined by

⛏️ P2SHANSXnLY2HX2a5e6fdcDUZDtfwTSd25TjkD

Merkle Root

14a8f3c46867475b5b438ce79b7a77591c841b60146d907be625fc643fada725
Transactions (1)
Coinbase14a8f3c4686747…25fc643fada725
1 in β†’ 1 out8.3800 XPM116 B
ANSXnLY2…Sd25TjkD
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.

3.112 Γ— 10⁹⁹(100-digit number)
31126473301774145895…12042198484649545279
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
3.112 Γ— 10⁹⁹(100-digit number)
31126473301774145895…12042198484649545279
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
3.112 Γ— 10⁹⁹(100-digit number)
31126473301774145895…12042198484649545281
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
6.225 Γ— 10⁹⁹(100-digit number)
62252946603548291791…24084396969299090559
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
6.225 Γ— 10⁹⁹(100-digit number)
62252946603548291791…24084396969299090561
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
1.245 Γ— 10¹⁰⁰(101-digit number)
12450589320709658358…48168793938598181119
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
1.245 Γ— 10¹⁰⁰(101-digit number)
12450589320709658358…48168793938598181121
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
2.490 Γ— 10¹⁰⁰(101-digit number)
24901178641419316716…96337587877196362239
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
2.490 Γ— 10¹⁰⁰(101-digit number)
24901178641419316716…96337587877196362241
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
4.980 Γ— 10¹⁰⁰(101-digit number)
49802357282838633433…92675175754392724479
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
4.980 Γ— 10¹⁰⁰(101-digit number)
49802357282838633433…92675175754392724481
Verify on FactorDB β†—Wolfram Alpha β†—
Difference: 2^4 Γ— origin + 1 βˆ’ 2^4 Γ— origin βˆ’ 1 = 2 (twin primes βœ“)
Level 5 β€” Twin Prime Pair (2^5 Γ— origin Β± 1)
2^5 Γ— origin βˆ’ 1
9.960 Γ— 10¹⁰⁰(101-digit number)
99604714565677266866…85350351508785448959
Verify on FactorDB β†—Wolfram Alpha β†—

What this block proved

The miner who found this block proved the existence of 11 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
RareChain length 11

Approximately 1 in 1,000 blocks. Noteworthy discoveries.

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:57,778,948 XPMΒ·at block #6,816,862 Β· updates every 60s
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