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Block #547,843

TWNLength 11β˜…β˜…β˜…β˜†β˜†

Bi-Twin Chain Β· Discovered 5/16/2014, 5:06:44 PM Β· Difficulty 10.9578 Β· 6,262,068 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
bdc67f40786b548bd5ebc896738ae0357e725cb899b8a77788a4cf84476b2229
View on Chainz β†—

Height

#547,843

Difficulty

10.957839

Transactions

1

Size

243 B

Version

2

Bits

0af534eb

Nonce

313,574,615

Timestamp

5/16/2014, 5:06:44 PM

Confirmations

6,262,068

Mined by

⛏️ P2SHARzmpY4cAhz8WiJkMBTqRELns6fvx8bF9t

Merkle Root

527b07ebe96a4dab7c8740f3eee8f0d975062b2de5008f2f45b36deb7b94313e
Transactions (1)
Coinbase527b07ebe96a4d…b36deb7b94313e
1 in β†’ 2 out8.3100 XPM152 B
ARzmpY4c…fvx8bF9tALPu3s2c…EJXLjVFh
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.

8.001 Γ— 10⁹⁷(98-digit number)
80014733309670583962…98351721257159875339
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
8.001 Γ— 10⁹⁷(98-digit number)
80014733309670583962…98351721257159875339
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
8.001 Γ— 10⁹⁷(98-digit number)
80014733309670583962…98351721257159875341
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
1.600 Γ— 10⁹⁸(99-digit number)
16002946661934116792…96703442514319750679
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
1.600 Γ— 10⁹⁸(99-digit number)
16002946661934116792…96703442514319750681
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
3.200 Γ— 10⁹⁸(99-digit number)
32005893323868233585…93406885028639501359
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
3.200 Γ— 10⁹⁸(99-digit number)
32005893323868233585…93406885028639501361
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
6.401 Γ— 10⁹⁸(99-digit number)
64011786647736467170…86813770057279002719
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
6.401 Γ— 10⁹⁸(99-digit number)
64011786647736467170…86813770057279002721
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
1.280 Γ— 10⁹⁹(100-digit number)
12802357329547293434…73627540114558005439
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
1.280 Γ— 10⁹⁹(100-digit number)
12802357329547293434…73627540114558005441
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
2.560 Γ— 10⁹⁹(100-digit number)
25604714659094586868…47255080229116010879
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:57,723,372 XPMΒ·at block #6,809,910 Β· updates every 60s
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AQZeJoQ81VgeHQBpEYTgvNqV1gnz3L5SvK

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