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Block #2,233,824

TWNLength 10β˜…β˜…β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 8/2/2017, 2:20:23 PM Β· Difficulty 10.9459 Β· 4,574,476 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
6ae33b39ab9afcfa52f65e4cec799a5b30a575ee874818e146e0a7b134484c78
View on Chainz β†—

Height

#2,233,824

Difficulty

10.945934

Transactions

2

Size

542 B

Version

2

Bits

0af228b4

Nonce

8,497,861

Timestamp

8/2/2017, 2:20:23 PM

Confirmations

4,574,476

Mined by

⛏️ P2SHAX7L5nbVTwXJWPjABeCVtmh38aJfbEnfxb

Merkle Root

9dee9bafa8d19c9bcb5841b180fe4439578a63c8d697cd7cead5512a175ab5ae
Transactions (2)
Coinbase7b5efe3ff9a7b3…dd223c2667f001
1 in β†’ 1 out8.3400 XPM110 B
AX7L5nbV…JfbEnfxb
283717dccee78a…63a223c13ce1fe
2 in β†’ 1 out2.2305 XPM342 B
Ab4MqTkK…LUmkVPqg
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.

2.736 Γ— 10⁹⁴(95-digit number)
27361126277128169062…41937789576188438399
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
2.736 Γ— 10⁹⁴(95-digit number)
27361126277128169062…41937789576188438399
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
2.736 Γ— 10⁹⁴(95-digit number)
27361126277128169062…41937789576188438401
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
5.472 Γ— 10⁹⁴(95-digit number)
54722252554256338124…83875579152376876799
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
5.472 Γ— 10⁹⁴(95-digit number)
54722252554256338124…83875579152376876801
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
1.094 Γ— 10⁹⁡(96-digit number)
10944450510851267624…67751158304753753599
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
1.094 Γ— 10⁹⁡(96-digit number)
10944450510851267624…67751158304753753601
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
2.188 Γ— 10⁹⁡(96-digit number)
21888901021702535249…35502316609507507199
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
2.188 Γ— 10⁹⁡(96-digit number)
21888901021702535249…35502316609507507201
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
4.377 Γ— 10⁹⁡(96-digit number)
43777802043405070499…71004633219015014399
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
4.377 Γ— 10⁹⁡(96-digit number)
43777802043405070499…71004633219015014401
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:57,710,453 XPMΒ·at block #6,808,299 Β· updates every 60s
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AQZeJoQ81VgeHQBpEYTgvNqV1gnz3L5SvK

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