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Block #1,503,647

TWNLength 10β˜…β˜…β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 3/19/2016, 12:42:35 PM Β· Difficulty 10.6508 Β· 5,304,744 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
a906f107e8d5d4a6019ecb677e7159af42dddcbe9d62d4cbd9efe7583087f63e
View on Chainz β†—

Height

#1,503,647

Difficulty

10.650770

Transactions

2

Size

3.70 KB

Version

2

Bits

0aa698d9

Nonce

1,415,113,246

Timestamp

3/19/2016, 12:42:35 PM

Confirmations

5,304,744

Mined by

⛏️ P2SHAG94ufgmzDbhEAuULHh7Qou5M1uDnfXyE4

Merkle Root

613a8e6dc203622ee69479eab80ee28b3241aab1399360fa73526c21b561aff0
Transactions (2)
Coinbase38784bdf31434e…5a8e7f19b450f2
1 in β†’ 1 out8.8486 XPM110 B
AG94ufgm…uDnfXyE4
8f2540b4491c24…e03cbec25e8353
24 in β†’ 1 out24.2100 XPM3.51 KB
AGGDUbaH…1rD1xH24
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.

3.174 Γ— 10⁹⁢(97-digit number)
31748279354151710263…08217170666420072959
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
3.174 Γ— 10⁹⁢(97-digit number)
31748279354151710263…08217170666420072959
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
3.174 Γ— 10⁹⁢(97-digit number)
31748279354151710263…08217170666420072961
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
6.349 Γ— 10⁹⁢(97-digit number)
63496558708303420526…16434341332840145919
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
6.349 Γ— 10⁹⁢(97-digit number)
63496558708303420526…16434341332840145921
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
1.269 Γ— 10⁹⁷(98-digit number)
12699311741660684105…32868682665680291839
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
1.269 Γ— 10⁹⁷(98-digit number)
12699311741660684105…32868682665680291841
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
2.539 Γ— 10⁹⁷(98-digit number)
25398623483321368210…65737365331360583679
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
2.539 Γ— 10⁹⁷(98-digit number)
25398623483321368210…65737365331360583681
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
5.079 Γ— 10⁹⁷(98-digit number)
50797246966642736421…31474730662721167359
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
5.079 Γ— 10⁹⁷(98-digit number)
50797246966642736421…31474730662721167361
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:57,711,184 XPMΒ·at block #6,808,390 Β· updates every 60s
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AQZeJoQ81VgeHQBpEYTgvNqV1gnz3L5SvK

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